If you were to drop a vertical line from G to the base, there would be a square on the right side with sides of length 24ft. On the left would be a right triangle with a hypotenuse of 30ft and a vertical leg to 24ft. It's base could then be found using the Pythagorean Theorem.
h^2=x^2+y^2, where h is the length of the hypotenuse of a right triangle and x and y are the side lengths. In this case we have:
30^2=24^2+b^2, b is the length of the base of the triangle on left side...
900=576+b^2
b^2=324
b=18 ft
So that base length must be added to 24 ft to get the total length of FJ so:
FJ=18+24=42ft